Efficiently Simulating the Benzene Molecule on Trapped-Ion Quantum Computers using a Variational Quantum Eigensolver with Unitary Coupled Cluster with Singles and Doubles

The unitary coupled cluster with singles and doubles (uCCSD) ansatz is among the first ansatze used with the variational quantum eigensolver (VQE) algorithm to provide accurate predictions of molecular energies. However, the largest publicly reported implementation on quantum hardware has been limited to simulations of molecules with a minimal active space. The main reason for this is that the uCCSD ansatz results in deep quantum circuits, making it impractical to run on current noisy quantum devices. Here, we apply a series of circuit optimization techniques to improve the compilation efficiency of the uCCSD ansatz, tailored to trapped-ion quantum devices. This includes taking advantage of all-to-all connectivity, efficient orbital-to-qubit mapping, optimal term ordering to maximally reduce the entangling gate count, and exploiting molecular point group symmetry.

Given these algorithmic improvements, we performed the simulation of a benzene molecule in a 4-electron, 4-orbital active space using uCCSD on IonQ’s Aria trapped-ion quantum computer. The 8-qubit circuit contains more than 138 entangling operations, which is among the deepest VQE circuits that ever run on quantum hardware. We find that the Aria quantum computer successfully finds the optimal set of circuit parameters, and predicts highly accurate relative energies. The results demonstrate Aria’s capabilities of running deep variational circuits for quantum chemistry simulations.